E-mount lens AF speed on Sony A6000

Hi,
I read somewhere that the SEL50f18 was one of the slower lenses to AF on the A6000, even with the latest firmware. To test that theory, I used AF-S and center point to focus on two different subjects (indoors during daytime with reasonable lighting about ISO 400 1/60 f4). I compared it to my 24-70/4 at about 50mm, as well as against the 70-200/4 at 70mm. What I found was that the 50/1.8 was definitely slower than the 24-70/4 and 70-200/4 with single point AF and AF-S (at f1.8 and f4 on 50/1.8 and f4 for the other two lenses), and I could see the lens still needing to adjust a few times to get to focus, whereas the new lenses just went straight to the focus.

Do note that the 50/1.8 focus on A6000 is definitely much better than on the earlier Nex cameras which were significantly slower. And I am thinking that maybe the slower AF with this lens can explain why my hit rates with the 50/1.8 lens when shooting pictures of my puppy outdoors in good light in AF-C had many frames which were not in focus (despite using auto ISO at 1/1000 s shutter speed to 'freeze motion'). Perhaps the choice of lens when shooting AF-C on A6000 is also very important in getting better hit rates. I only have these 3 E-mount lenses, so can't comment on others.

The other interesting thing is that I also compared AF-S with the 24-70/4 & 70-200/4 A6000 vs A7R and did not feel there was that much difference in AF speed between them with instant movement to the sharpest focus; definitely not to the same level of lag as experienced when comparing these newer lenses against the 50/1.8 on the A6000. I wonder if the Zeiss 55/1.8 has faster AF speed than the 50/1.8? Anyone else noted the same experience with difference in AF speed between their E-mount lenses on the A6000? It would be good to share on which lenses we feel focuses fastest on the A6000.
Boon